In a small bowl, dissolve yeast in warm water; let sit for 10 minutes.
In stand mixer bowl, add flour, sugar, salt and shortening/butter; mix with pastry blender or fork.. In saucepan or microwave-safe dish, heat milk to 110-115°F. Add yeast mixture and warm milk to flour mixture. Using a paddle attachment, blend on low speed for 30 seconds. Add egg yolk; beat on medium speed for 3 minutes.
Cover bowl with waxed paper, then foil. Chill in refrigerator for 2 hours to not more than 48 hours.
Prepare Fillings before removing dough from refrigerator. (See below for filling variations.)
Divide dough into 2 equal parts. Beat egg white until stiff. Roll dough on lightly floured board into a 6x18-inch rectangle. Spread with 1/2 the egg white, then one of the Fillings. Fold one long edge over to other side, pinch edge of dough into roll. Handle Kringle carefully- this is a tender dough. Place on lightly greased baking sheet in horseshoe or circular shape. Shape second Kringle and place on second baking sheet. Cover; let rise until almost doubled, about 30-40 minutes.
Preheat oven to 400°F.
Bake for 18 to 25 minutes. Remove from pans; cool on racks.
Glaze: Combine ingredients in small mixing bowl; beat until smooth. Add more/less powdered sugar to achieve desired consistency.
Before serving, drizzle glaze over the top of the Kringle.